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Preserving user-friendly shadow and high-contrast quality for multiple visual secret sharing technique
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Preserving user-friendly shadow and high-contrast quality for multiple visual secret sharing technique
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Jung-San Lee , Chin-Chen Chang
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, Ngoc-Tu Huynh
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, Hsin-Yi Tsai
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Department of Information Engineering and Computer Science, Feng Chia University, Taichung, 40724, Taiwan, ROC b Department of Computer Science and Information Engineering, Asia University, Taichung, 41354, Taiwan, ROC c Department of Computer Science, National Tsing Hua University, 30013 No. 101, Section 2, Kuang-Fu Road, Hsinchu, 30013, Taiwan, ROC d College of Information Technology, The University of Danang, Danang University Village, Luu Quang Vu Street, Danang, Viet Nam
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Keywords: Visual secret sharing Visual cryptography Pixel expansion User-friendly
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Traditional secret sharing scheme that encrypts secret image based on mathematical calculation to construct shadows often requires the complicated computation to extract the secret. Later on, conventional visual cryptography scheme was developed to deal with the perplexed calculation in encryption and extraction of previous schemes. The stack-to-see technique can be used easily to reveal the secret by human visual system, which can shorten computation time. However, the expansion of image size and the noise-liked shares of previous schemes lead to the difficulty in transmission and storage. This study uses a pre-defined codebook to encode two secret images into two meaningful transparencies without pixel expansion. According to the turning mechanism, two secret images can be embedded into two shares simultaneously. The decryption process allows the user to get two secrets via turning and stacking. A notable feature of our scheme is that the black pixel value of the secret image can be completely extracted and the vision quality of stacking results can be identified clearly. © 2015 Elsevier Inc. All rights reserved.
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1. Introduction
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Visual cryptography (VC) was first proposed by Naor and Shamir in 1994 [1]. The concept of visual cryptography technique was based on the secret sharing scheme presented by Shamir in 1979 [2]. The main idea of secret sharing is that more than a predefined number of participants can cooperate to reveal the original ciphertext; otherwise nothing about the secret can be extracted. In fact, to conceal or reveal the original secret in a secret sharing mechanism needs the adoption of complicated computation. The completion of the computation requires the help of computers. But in the real world, we often face the situation that we cannot access to a computer to figure out any secret information. So, the new thought of reducing the computation was studied. The idea of visual cryptography is to encrypt a binary secret image into k noise-like shadows which exhibit no private message [2,5–14]. As similar as (k, n)-threshold secret sharing scheme, the visual cryptography mechanism follows the regulation which requires k (k ≤ n) shadows to decode confidential information
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E-mail address: [email protected] (J.-S. Lee). http://dx.doi.org/10.1016/j.dsp.2015.02.012 1051-2004/© 2015 Elsevier Inc. All rights reserved.
by superimposing these shadows through human visual system (HVS). Nevertheless, k − 1 or fewer shadows are insufficient to generate confidential message or to leak any private information. In traditional visual cryptography, the original gray-level secret image needs to be transformed into a halftone image. Then it is encoded by expanding the halftone secret image to achieve the goal of camouflaging the original secret image without any information leaked out. The following is a simple example. A white pixel 1 can be encoded into two shadows by randomly choosing one row of white-pixel in Table 1; whereas a black pixel 2 is selected from the row of black-pixel in Table 1 randomly. Since each pixel in secret can be encoded into one block of the combination of black and white pixel, the shadows are cluttered to achieve the confusion of visibility. Extracting the secret by stacking two shadows, we can acquire similar outcome of the original secret. As the human vision is not sensitive to the contrast that makes human eye be able to identify the content of secret from the stacking result. Fig. 1 shows the results of Naor and Shamir’s visual cryptography scheme by expanding one pixel to two pixels. The result of Naor– Shamir’s method clearly shows that an individual shadow reveals nothing, while the stacking result of two shadows can be used to identify the content of secret.
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Fig. 1. Results of Naor and Shamir’s visual cryptography scheme with pixel expansion = 2.
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Table 1 Naor and Shamir’s visual cryptography scheme with pixel expansion = 2.
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Block in shadow1
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Fig. 2. An example of turning image over with horizontal mechanism.
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Naor and Shamir’s scheme is really practical for encrypting secret and decreasing the computing ability. Nevertheless, the burden of storage is heavy due to the expanding of original image size. In 2004, Yang [4] used the concept of pre-calculating the probabilities of white pixels in bright and dark areas of secret for encrypting secret without pixel expansion. Based on the probabilities of calculating the contrast difference, an encoding rule was used to create shadows. After stacking transparencies, the high contrast of stacking results is shown clearly. In 2009, Shyu [12] used the random grids technique to encrypt one halftone secret image without expanding pixels of secret. In 2010, Yang and Ciou [5] proposed a hybrid technique combining two different sharing methods: Visual cryptography scheme and polynomial-based image secret sharing scheme. The secret image can be revealed by the concept of stackto-see, while the original secret can be extracted losslessly. In 2011, Hou and Quan [15] proposed a progressive visual cryptography scheme by using the secret sharing matrices. In Hou and Quan’s scheme, N shadows are generated for different participants. The exhibition of ciphertext is proportional to the number of gathered shadows. Although traditional visual cryptography refused any computation during decryption, its limitation is to hold a noise-like shadow. The meaningless transparencies are not user-friendly with difficulty for identification and management. Therefore, meaningful shadows become the trend of visual cryptography. Fang [14] proposed a friendly progressive method by using a coded sharing codebook. In Fang’s scheme, one pixel value is expanded into a 2 × 2 pixel block to get a meaningful transparency. The decoding way is to superimpose transparencies gradually so that the secret image can be revealed more and more clearly. In other hands, sharing only one confidential message is not efficient. In order to solve the shortcoming, many scholars have proposed multiple secret sharing methods [17,18], which increased the number of secrets to be shared at the same time. Wu and Chen [18] proposed a multiple secret sharing scheme to embed two secret images into two shadows. Two sets of secret can be embedded by rotating a specific shadow. To reveal the first secret, we stack two shadows. Second secret becomes visible if the first shadow is rotated counterclockwise, and stacked together with the second shadow. Inspired by Feng et al.’s definition [16] and the above-mentions, to reduce the size of the expanded visual cryptography with meaningful shadows is the most important issue in our study. In addition, the new method aims to provide a high contrast of stacking results, which means the stacking result can show a complete black pixel value of secret images. Thus the secret image can be evidently recognized by the human vision. In this paper, the codebook is compiled for encoding meaningful transparencies without pixel expansion. Furthermore, two secret images are embedded
into two shadows by the turning over mechanism. Note that the first secret image is displayed by superimposing the first and the second transparency, while the second secret image is extracted by turning the first transparency with horizontal technique to stack onto the second transparency. Fig. 2 illustrates an example of turning over mechanism. The remainder of this paper is organized as follows. In Section 2, the meaningful visual cryptography scheme is described detailedly. Experimental results of the proposed scheme are shown in Section 3. Finally, Section 4 gives the conclusions of this paper.
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2. The proposed method
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First, we design an opaque visual cryptography codebook for two secret images (S 1 and S 2 ) to be embedded into two transparencies (T 1 and T 2 ). Opaque means the stacking result of two shared images can reveal complete black pixel in the secret. As to the decoding process, the decrypted secret image S 1 can be revealed by stacking T 1 with T 2 and the decrypted secret image S 2 is decoded by turning T 1 over and stacking onto T 2 . When two meaningful shared images (T 1 and T 2 ) are gathered, the OR operation is adopted to stack two pixel values in two transparencies. Here, we define the black pixel as 0 and white pixel as 1. The stacking operation for two meaningful shared images is symbolized by ⊕, where 0 ⊕ 0 = 0, 0 ⊕ 1 = 1, 1 ⊕ 0 = 1, and 1 ⊕ 1 = 1. Here, Fig. 3 shows the decrypting operation of the proposed scheme and two secret images are revealed by stacking two transparencies. The size of each image is M × N and two pixel values in each image are called a symmetric pair which two pixels are turning over with horizontal in relative position. For two symmetric pairs in different decrypted secret images, four pixel values must be considered simultaneously to satisfy the following conditions:
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S 1 (i , N − j + i ) = T 1 (i , N − j + i ) ⊕ T 2 (i , N − j + i ),
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S 2 (i , j ) = T 1 (i , N − j + i ) ⊕ T 2 (i , j ),
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S 1 (i , j ) = T 1 (i , j ) ⊕ T 2 (i , j ),
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(1)
Every four-pixel values of secret images T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )] should be encoded at the same time. To restrict the complete black pixel of stacking results, two halftone secret images are encoded into two transparencies by an opaque-oriented codebook. Table 2 shows all possible encoding sets for two transparencies that the corresponding results can be chosen for constructing an opaque codebook.
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Fig. 3. Stacking two transparencies T 1 and T 2 sized M × N to decrypt secret images S 1 and S 2 by OR operation.
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Table 2 All possible encoding sets T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )]
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According to Table 2, we want to guarantee the stacking result with opaque outcome of black pixel for superimposing two transparencies, in which we need to check the entire black pixel in the generated result and to pick out the satisfied encoding set from Table 2 for each generating matrix. The following is an example for choosing a suitable candidate outcome. Suppose that we get a stacking result S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )] is equal to 1212. It means the encoding sets satisfy the condition that two pixels value S 1 (i , N − j + i ) and S 2 (i , N − j + i ) are black. By checking Table 2, we observe that the encoding set T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )] would be 1112, 2211, 2112, 1212, 1122, 1222, 2122, 2212, 2221, and 2222. Based on the regulation, we can construct opaque-oriented codebook for encoding matrices corresponding to the 24 = 16 combinations of S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )] since the possible value of each pixel is Black or White.
In Table 3, we collect all the satisfied codewords for each combination to build Encoding matrices. To construct Table 3, firstly, we have to determine which pixels in the stacking results are Black ones. Then, we select from Table 2 all the candidate codewords and gather them to form the matrices. From these encoding matrices, we can randomly select sub-matrices and classify into Black or While pool to construct two transparencies. When the opaque-oriented codebook is constructed, the details of the encryption algorithm are described as below:
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Step 1: Apply the halftone technique to transform two secret im×N into ages sized M × N and the cover image sized M2× 2 the binary images. Simultaneously, divide two secret imN ages sized M × into 2 × 2 non-overlapping blocks and its 2 corresponding symmetric pairs into 2 × 2 non-overlapping blocks. Mark the left part blocks as LBLxj and the right part
N blocks as where j = 1, 2, · · · , M × and x = 1, 2. 2 Create the vectors [LP1i , RP 1i , LP 2i , RP 2i ], i = 1, 2, 3, 4, where LP 1i and LP 2i are the pixel values of LBL1j and LBL2j , respectively; RP 1i and RP 2i are the pixel values of RBL1j and RBL2j , respectively. Use each [LP 1i , RP 1i , LP 2i , RP 2i ] as
RBLxj ,
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S = [ S 1 (i , j ), S (i , N − j + i ), S 2 (i , j ), S (i , N − j + i )] to 1 2 construct the corresponding encoding matrix EMk , k = 1, 2, 3, 4, from Table 3.
Step 3: Apply each EMk with other distinct encoding matrices to construct a four values matching-matrix MM y , y = 1, 2, 3, . . . , Size(EM1 ) × Size(EM2 ) × Size(EM3 ) × Size(EM4 ). Matching matrix MM y is the candidate matrix chosen among 16 matrices to be distributed into Black-pool or White-pool [10]. If the number of non-zero pixel values in one block of MM y is less than 2, we add this matrix into Black-pool; otherwise, it is added to White-pool. For the next step, according to the pixel of cover halftone image, we select a matrix in Black-pool of White-pool to form the transparencies. The function of Size(•) is to compute the number of the rows in EMk . Then, MM y can be distributed
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Fig. 4. 512 × 512 two secret images.
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pool will be selected. Then, choose one result in the pool randomly to form the two transparencies. N Step 5: Increase j by one. If j is not equal to M × , repeat Step 2 2 until all blocks are processed.
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The proposed method can be decrypted without any computation and the secret is easily to be interpreted by the human perception. Users only need to gather two secret images to photocopy them onto transparencies and perform stack-to-see mechanism to get the first secret image. The second secret image can be extracted by turning over the first transparency and superimpose it onto the other one. Finally, the operation of decryption is performed to show the secrets by the meaningful transparencies.
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3. Experimental results
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In this section, we conducted the simulation of the proposed scheme to show the performance. Fig. 4 shows the 512 × 512 binary secret images. Fig. 5 exhibits twelve 256 × 256 gray-level images used as cover images to achieve the goal of meaningful shares, i.e., Barbara, Baboon, Goldhill, Lena, Peppers, Sailboat, Bridge, Cameraman, Elaine, Tank, View, and Man. The result of twelve cover images preprocessed by the halftone technique is shown in Fig. 6. In this paper, we generate two meaningful transparencies to share two secret images at the same time via turning and stacking mechanism. Therefore, the scheme preserves the user-friendly property of visual secret sharing techniques. Moreover, the method which satisfies four general criteria for VSS scheme, that is, security, accuracy, computational complexity and shadow size, also called pixel expansion. The experimental results to demonstrate our achievements related to these criteria are presented in Sections 3.1, 3.2, 3.3 and 3.4.
⎞ ⎛ 1122 ⎟ ⎜1221 2112 ⎟ ⎜ ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222 ⎛ ⎞ 1122 ⎜1222⎟ ⎜2112⎟ ⎜2122⎟ ⎜2211⎟ ⎜ ⎟ ⎝2212⎠ 2221 2222 ⎛
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⎞ 1122 ⎜1221⎟ ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222
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Condition 1:black-pool, if 0 ≤ HW (MM y ) < 2, Condition 2:white-pool, if 2 ≤ HW (MM y ) ≤ 4,
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3.1. Security analysis
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into black-pool or white-pool. The distribution algorithm is performed under the following conditions.
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Table 3 The 16 combinations of encoding matrices for two symmetric pairs S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )].
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where the function of HW (•) is to compute the number of non-zero pixel values in one block. Step 4: Based on the halftone cover image, the black or white pixel in the cover image for deciding the black-pool or white-
The security of our proposed scheme is based on two factors: the meaningfulness of shadows (or also called transparencies) to avoid suspicion from attacker and the randomness of selecting codewords in encoding matrices to form transparencies. Table 4 illustrates the experimental results of the proposed scheme with two meaningful shadows: Shadow1 and Shadow2. The first two columns list the shadows sized 512 × 512, in which we have encrypted two secret images into shadows with our designed codebook. Without any computation, we can superimpose Shadow1 onto Shadow2 to extract the first secret image as Fig. 4(a). By turning Shadow1 over with horizontal and stacking it onto Shadow2, the second secret image can be exposed as in Fig. 4(b). Here, the last two columns show the stacking results of two shadows. Furthermore, the probabilities distribution of codewords selected from the encoding matrix are fluctuated from 1/7 ≈ 14.2% (for the case of all pixels are BLACK) to 1/12 ≈ 8.3%, it is a very small variance to judge the full secret images. Therefore, no matter what codewords or sub-matrices are chosen, the secret images cannot be revealed.
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3.2. Accuracy
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To achieve the accuracy of stacking results, our method preserves the opaque of secret images. In other words, to generate the encoding set, we check the entire Black pixels in the stacking results to form Table 2, and then create the encoding matrices by picking out satisfied encoding set from Table 2. Therefore, it can be seen from the stacking results in Table 4 that our proposed scheme completely reveals the original secret images. From the experiments, the stacking results can exactly show the intact of black pixel values in secret images. According to the codebook, two secrets can be revealed clearly. With the construction of the
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To demonstrate that the proposed scheme requires a very low computational cost, we analyze the scheme in two procedures: share construction procedure and revealing procedure.
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– In share construction procedure, we first generate the possible encoding sets. This step is to figure out all the combination of
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the group of 4 pixels, thus, the time complexity of this step is O (n). The next step in this procedure is to find the suitable matching solution to form the encoding matrices. It is obvious that this step spends O (n). Therefore, these steps require very low time consuming. – In the revealing procedure, the secrets are constructed without any extra computations. We reveal the secret by simply turning and stacking steps.
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In summary, our scheme has low computational cost. Thus, it is suitable for real-time applications.
3.4. Pixel expansion
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From our share construction phase, the scheme shares two secret images at the same time without causing pixel expansion problem. In other words, the shadows generated by our scheme have the same size with the original ones. Finally, the comparisons between related works and the proposed method in terms of four different features are shown in Table 5. Only Fang’s method has to expand the size of original secret. Our scheme cannot only eliminate the defect of expanding original secret size, but also embed more than one secret into two
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Table 5 Performance comparisons with other schemes.
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Naor and Shamir [1]
Fang [14]
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Lin et al. [10]
Proposed scheme
4 Yes Meaningless Human Visual System 1
4 Yes Meaningful Human Visual System 1
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1 Yes Meaningless Human Visual System 2
1 Yes Meaningful Human Visual System 2
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4. Conclusions
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According to the designed codebook, an encoding technique with user-friendly shadows is proposed in this paper. This can greatly help reducing the potential risk from malicious attackers. In particular, the pixel expanding problem is absent from the proposed method. With the stack-to-see method for decoding two secrets, the whole decoding operation uses non-computation operation for combining two transparencies. Experimental results show that the complete black pixel value can be laid out to highlight the contrast to clarify the secret.
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[14] W.P. Fang, Friendly progressive visual secret sharing, Pattern Recognit. 41 (4) (2008) 1410–1414. [15] Y.C. Hou, Z.Y. Quan, Progressive visual cryptography with unexpanded shares, IEEE Trans. Circuits Syst. Video Technol. 21 (11) (2011) 1760–1764. [16] L. Feng, C.K. Wu, X.J. Lin, A new definition of the contrast of visual cryptography scheme, Inf. Process. Lett. 110 (2010) 241–246. [17] T.H. Chen, C.S. Wu, Efficient multi-secret image sharing based on Boolean operations, Signal Process. 91 (2011) 90–97. [18] C.C. Wu, L.H. Chen, A study on visual cryptography, M.S. thesis, Institute of Computer and Information Science, National Chiao Tung University, Hsinchu, Taiwan, 1998.
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[3]
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References
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Jung-San Lee has worked as an associate professor in the Department of Information Engineering and Computer Science at Feng Chia University, Taichung, Taiwan. His current research interests include information security, image processing, and watermarking.
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transparencies. As to the other two schemes, even they can get rid of the problem of pixel expansion, they cannot offer meaningful shadows to prevent from potential risk.
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[1] N. Naor, A. Shamir, Visual cryptography, in: Advances in Cryptography Eurocypt, Springer-Verlag, Berlin, 1994, pp. 1–12. [2] A. Shamir, How to share a secret, Commun. ACM 22 (11) (1979) 612–613. [3] C.C. Thien, J.C. Lin, An image-sharing method with user-friendly shadow images, IEEE Trans. Circuits Syst. Video Technol. 13 (12) (2003) 1161–1169. [4] C.N. Yang, New visual secret sharing schemes using probabilistic method, Pattern Recognit. Lett. 25 (4) (2004) 481–494. [5] C.N. Yang, C.B. Ciou, Image secret sharing method with two-decoding-options: lossless recovery and previewing capability, Image Vis. Comput. 28 (12) (2010) 1600–1610. [6] D. Jin, W.Q. Yan, M.S. Kankanhalli, Progressive color visual cryptography, J. Electron. Imaging 14 (3) (2005) 033019-1–033019-13. [7] F. Liu, C.K. Wu, X.J. Lin, Colour visual cryptography schemes, IET Inf. Secur. 2 (4) (2008) 151–165. [8] K.H. Lee, P.L. Chiu, A high contrast and capacity efficient visual cryptography scheme for the encryption of multiple secret images, Opt. Commun. 284 (12) (2011) 2730–2741. [9] S. Cimato, R. De Prisco, A. De Santis, Colored visual cryptography without color darkening, Theor. Comput. Sci. 374 (1–3) (2007) 261–276. [10] S.J. Lin, S.K. Chen, J.C. Lin, Flip visual (FVC) with perfect security, conditionallyoptimal contrast, and no expansion, J. Vis. Commun. Image Represent. 21 (8) (2010) 900–916. [11] S.J. Shyu, K. Chen, Visual multiple secret sharing based upon turn and flipping, Inf. Sci. 181 (5) (2011) 3246–3266. [12] S.J. Shyu, Image encryption by multiple random grids, J. Pattern Recognit. 42 (7) (2009) 1582–1596. [13] S.J. Lin, J.C. Lin, VCPSS: a two-in-one two-decoding-options image sharing method combining visual cryptography (VC) and polynomial-style sharing (PSS) approaches, Pattern Recognit. 40 (12) (2007) 3652–3666.
Chin-Chen Chang is a Fellow of IEEE, a Fellow of IEE and a member of the Chinese Language Computer Society, the Chinese Institute of Engineers of the Republic of China, and the Phi Tau Phi Society of the Republic of China. His research interests include computer cryptography and image compression.
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Ngoc-Tu Huynh received the M.S. degree in 2010 from Feng Chia University. Since 2006, she has been a Lecturer of Department of Computer Science, College of Information Technology, Da Nang University, Vietnam. She is currently pursuing her Ph.D. in Information Engineering and Computer Science, Feng Chia University, Taichung, Taiwan. Her research interests include visual secret sharing, and image processing.
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Hsin-Yi Tsai has received the B.S. degree in computer science in 2012 from National Tsing Hua University, Taiwan. Her current research interests include information security and visual secret sharing.
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Preserving user-friendly shadow and high-contrast quality for multiple visual secret sharing technique
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Jung-San Lee , Chin-Chen Chang
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Department of Information Engineering and Computer Science, Feng Chia University, Taichung, 40724, Taiwan, ROC b Department of Computer Science and Information Engineering, Asia University, Taichung, 41354, Taiwan, ROC c Department of Computer Science, National Tsing Hua University, 30013 No. 101, Section 2, Kuang-Fu Road, Hsinchu, 30013, Taiwan, ROC d College of Information Technology, The University of Danang, Danang University Village, Luu Quang Vu Street, Danang, Viet Nam
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Keywords: Visual secret sharing Visual cryptography Pixel expansion User-friendly
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Traditional secret sharing scheme that encrypts secret image based on mathematical calculation to construct shadows often requires the complicated computation to extract the secret. Later on, conventional visual cryptography scheme was developed to deal with the perplexed calculation in encryption and extraction of previous schemes. The stack-to-see technique can be used easily to reveal the secret by human visual system, which can shorten computation time. However, the expansion of image size and the noise-liked shares of previous schemes lead to the difficulty in transmission and storage. This study uses a pre-defined codebook to encode two secret images into two meaningful transparencies without pixel expansion. According to the turning mechanism, two secret images can be embedded into two shares simultaneously. The decryption process allows the user to get two secrets via turning and stacking. A notable feature of our scheme is that the black pixel value of the secret image can be completely extracted and the vision quality of stacking results can be identified clearly. © 2015 Elsevier Inc. All rights reserved.
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1. Introduction
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Visual cryptography (VC) was first proposed by Naor and Shamir in 1994 [1]. The concept of visual cryptography technique was based on the secret sharing scheme presented by Shamir in 1979 [2]. The main idea of secret sharing is that more than a predefined number of participants can cooperate to reveal the original ciphertext; otherwise nothing about the secret can be extracted. In fact, to conceal or reveal the original secret in a secret sharing mechanism needs the adoption of complicated computation. The completion of the computation requires the help of computers. But in the real world, we often face the situation that we cannot access to a computer to figure out any secret information. So, the new thought of reducing the computation was studied. The idea of visual cryptography is to encrypt a binary secret image into k noise-like shadows which exhibit no private message [2,5–14]. As similar as (k, n)-threshold secret sharing scheme, the visual cryptography mechanism follows the regulation which requires k (k ≤ n) shadows to decode confidential information
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E-mail address: [email protected] (J.-S. Lee). http://dx.doi.org/10.1016/j.dsp.2015.02.012 1051-2004/© 2015 Elsevier Inc. All rights reserved.
by superimposing these shadows through human visual system (HVS). Nevertheless, k − 1 or fewer shadows are insufficient to generate confidential message or to leak any private information. In traditional visual cryptography, the original gray-level secret image needs to be transformed into a halftone image. Then it is encoded by expanding the halftone secret image to achieve the goal of camouflaging the original secret image without any information leaked out. The following is a simple example. A white pixel 1 can be encoded into two shadows by randomly choosing one row of white-pixel in Table 1; whereas a black pixel 2 is selected from the row of black-pixel in Table 1 randomly. Since each pixel in secret can be encoded into one block of the combination of black and white pixel, the shadows are cluttered to achieve the confusion of visibility. Extracting the secret by stacking two shadows, we can acquire similar outcome of the original secret. As the human vision is not sensitive to the contrast that makes human eye be able to identify the content of secret from the stacking result. Fig. 1 shows the results of Naor and Shamir’s visual cryptography scheme by expanding one pixel to two pixels. The result of Naor– Shamir’s method clearly shows that an individual shadow reveals nothing, while the stacking result of two shadows can be used to identify the content of secret.
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Fig. 1. Results of Naor and Shamir’s visual cryptography scheme with pixel expansion = 2.
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Table 1 Naor and Shamir’s visual cryptography scheme with pixel expansion = 2.
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Fig. 2. An example of turning image over with horizontal mechanism.
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Naor and Shamir’s scheme is really practical for encrypting secret and decreasing the computing ability. Nevertheless, the burden of storage is heavy due to the expanding of original image size. In 2004, Yang [4] used the concept of pre-calculating the probabilities of white pixels in bright and dark areas of secret for encrypting secret without pixel expansion. Based on the probabilities of calculating the contrast difference, an encoding rule was used to create shadows. After stacking transparencies, the high contrast of stacking results is shown clearly. In 2009, Shyu [12] used the random grids technique to encrypt one halftone secret image without expanding pixels of secret. In 2010, Yang and Ciou [5] proposed a hybrid technique combining two different sharing methods: Visual cryptography scheme and polynomial-based image secret sharing scheme. The secret image can be revealed by the concept of stackto-see, while the original secret can be extracted losslessly. In 2011, Hou and Quan [15] proposed a progressive visual cryptography scheme by using the secret sharing matrices. In Hou and Quan’s scheme, N shadows are generated for different participants. The exhibition of ciphertext is proportional to the number of gathered shadows. Although traditional visual cryptography refused any computation during decryption, its limitation is to hold a noise-like shadow. The meaningless transparencies are not user-friendly with difficulty for identification and management. Therefore, meaningful shadows become the trend of visual cryptography. Fang [14] proposed a friendly progressive method by using a coded sharing codebook. In Fang’s scheme, one pixel value is expanded into a 2 × 2 pixel block to get a meaningful transparency. The decoding way is to superimpose transparencies gradually so that the secret image can be revealed more and more clearly. In other hands, sharing only one confidential message is not efficient. In order to solve the shortcoming, many scholars have proposed multiple secret sharing methods [17,18], which increased the number of secrets to be shared at the same time. Wu and Chen [18] proposed a multiple secret sharing scheme to embed two secret images into two shadows. Two sets of secret can be embedded by rotating a specific shadow. To reveal the first secret, we stack two shadows. Second secret becomes visible if the first shadow is rotated counterclockwise, and stacked together with the second shadow. Inspired by Feng et al.’s definition [16] and the above-mentions, to reduce the size of the expanded visual cryptography with meaningful shadows is the most important issue in our study. In addition, the new method aims to provide a high contrast of stacking results, which means the stacking result can show a complete black pixel value of secret images. Thus the secret image can be evidently recognized by the human vision. In this paper, the codebook is compiled for encoding meaningful transparencies without pixel expansion. Furthermore, two secret images are embedded
into two shadows by the turning over mechanism. Note that the first secret image is displayed by superimposing the first and the second transparency, while the second secret image is extracted by turning the first transparency with horizontal technique to stack onto the second transparency. Fig. 2 illustrates an example of turning over mechanism. The remainder of this paper is organized as follows. In Section 2, the meaningful visual cryptography scheme is described detailedly. Experimental results of the proposed scheme are shown in Section 3. Finally, Section 4 gives the conclusions of this paper.
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2. The proposed method
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First, we design an opaque visual cryptography codebook for two secret images (S 1 and S 2 ) to be embedded into two transparencies (T 1 and T 2 ). Opaque means the stacking result of two shared images can reveal complete black pixel in the secret. As to the decoding process, the decrypted secret image S 1 can be revealed by stacking T 1 with T 2 and the decrypted secret image S 2 is decoded by turning T 1 over and stacking onto T 2 . When two meaningful shared images (T 1 and T 2 ) are gathered, the OR operation is adopted to stack two pixel values in two transparencies. Here, we define the black pixel as 0 and white pixel as 1. The stacking operation for two meaningful shared images is symbolized by ⊕, where 0 ⊕ 0 = 0, 0 ⊕ 1 = 1, 1 ⊕ 0 = 1, and 1 ⊕ 1 = 1. Here, Fig. 3 shows the decrypting operation of the proposed scheme and two secret images are revealed by stacking two transparencies. The size of each image is M × N and two pixel values in each image are called a symmetric pair which two pixels are turning over with horizontal in relative position. For two symmetric pairs in different decrypted secret images, four pixel values must be considered simultaneously to satisfy the following conditions:
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S 1 (i , N − j + i ) = T 1 (i , N − j + i ) ⊕ T 2 (i , N − j + i ),
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(1)
Every four-pixel values of secret images T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )] should be encoded at the same time. To restrict the complete black pixel of stacking results, two halftone secret images are encoded into two transparencies by an opaque-oriented codebook. Table 2 shows all possible encoding sets for two transparencies that the corresponding results can be chosen for constructing an opaque codebook.
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Table 2 All possible encoding sets T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )]
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According to Table 2, we want to guarantee the stacking result with opaque outcome of black pixel for superimposing two transparencies, in which we need to check the entire black pixel in the generated result and to pick out the satisfied encoding set from Table 2 for each generating matrix. The following is an example for choosing a suitable candidate outcome. Suppose that we get a stacking result S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )] is equal to 1212. It means the encoding sets satisfy the condition that two pixels value S 1 (i , N − j + i ) and S 2 (i , N − j + i ) are black. By checking Table 2, we observe that the encoding set T = [ T 1 (i , j ), T 1 (i , N − j + i ), T 2 (i , j ), T 2 (i , N − j + i )] would be 1112, 2211, 2112, 1212, 1122, 1222, 2122, 2212, 2221, and 2222. Based on the regulation, we can construct opaque-oriented codebook for encoding matrices corresponding to the 24 = 16 combinations of S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )] since the possible value of each pixel is Black or White.
In Table 3, we collect all the satisfied codewords for each combination to build Encoding matrices. To construct Table 3, firstly, we have to determine which pixels in the stacking results are Black ones. Then, we select from Table 2 all the candidate codewords and gather them to form the matrices. From these encoding matrices, we can randomly select sub-matrices and classify into Black or While pool to construct two transparencies. When the opaque-oriented codebook is constructed, the details of the encryption algorithm are described as below:
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Step 1: Apply the halftone technique to transform two secret im×N into ages sized M × N and the cover image sized M2× 2 the binary images. Simultaneously, divide two secret imN ages sized M × into 2 × 2 non-overlapping blocks and its 2 corresponding symmetric pairs into 2 × 2 non-overlapping blocks. Mark the left part blocks as LBLxj and the right part
N blocks as where j = 1, 2, · · · , M × and x = 1, 2. 2 Create the vectors [LP1i , RP 1i , LP 2i , RP 2i ], i = 1, 2, 3, 4, where LP 1i and LP 2i are the pixel values of LBL1j and LBL2j , respectively; RP 1i and RP 2i are the pixel values of RBL1j and RBL2j , respectively. Use each [LP 1i , RP 1i , LP 2i , RP 2i ] as
RBLxj ,
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S = [ S 1 (i , j ), S (i , N − j + i ), S 2 (i , j ), S (i , N − j + i )] to 1 2 construct the corresponding encoding matrix EMk , k = 1, 2, 3, 4, from Table 3.
Step 3: Apply each EMk with other distinct encoding matrices to construct a four values matching-matrix MM y , y = 1, 2, 3, . . . , Size(EM1 ) × Size(EM2 ) × Size(EM3 ) × Size(EM4 ). Matching matrix MM y is the candidate matrix chosen among 16 matrices to be distributed into Black-pool or White-pool [10]. If the number of non-zero pixel values in one block of MM y is less than 2, we add this matrix into Black-pool; otherwise, it is added to White-pool. For the next step, according to the pixel of cover halftone image, we select a matrix in Black-pool of White-pool to form the transparencies. The function of Size(•) is to compute the number of the rows in EMk . Then, MM y can be distributed
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⎞ ⎛ 1121 ⎟ ⎜2111 ⎜1122⎟ ⎜1221⎟ ⎜1222⎟ ⎜2112⎟ ⎟ ⎜ ⎜2121⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222
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1111 ⎜1112⎟ ⎜1121⎟ ⎜1211⎟ ⎜2111⎟ ⎟ ⎜ ⎜2211⎟ ⎜2121⎟ ⎜2112⎟ ⎟ ⎜ ⎝1212⎠ 1122 1221 ⎞ ⎛ 1112 ⎟ ⎜2111 1122 ⎟ ⎜ ⎜2121⎟ ⎜1222⎟ ⎜2112⎟ ⎟ ⎜ ⎜1212⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222 ⎞ ⎛ 1121 1122 ⎜1211⎟ ⎟ ⎜ ⎜1212⎟ ⎜1221⎟ ⎜1222⎟ ⎟ ⎜ ⎜2121⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222 ⎞ ⎛ 1122 ⎟ ⎜1212 ⎜1222⎟ ⎜2121⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222 ⎞ ⎛ 1122 ⎜1211⎟ ⎜1212⎟ ⎜1221⎟ ⎜1222⎟ ⎟ ⎜ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222 ⎞ ⎛ 1112 ⎜1122⎟ ⎜1212⎟ ⎜1222⎟ ⎜2112⎟ ⎟ ⎜ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222 ⎞ ⎛ 1122 ⎜1211⎟ ⎜1212⎟ ⎜1221⎟ ⎜1222⎟ ⎟ ⎜ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222 ⎛ ⎞ 1122 ⎜1212⎟ ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎜ ⎟ ⎝2212⎠ 2221 2222
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Fig. 4. 512 × 512 two secret images.
⎞ 2111 ⎜1122⎟ ⎜1222⎟ ⎜2112⎟ ⎜1212⎟ ⎟ ⎜ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222 ⎞ 1121 1122 ⎟ ⎜ ⎜1221⎟ ⎜1222⎟ ⎜2121⎟ ⎟ ⎜ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222
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pool will be selected. Then, choose one result in the pool randomly to form the two transparencies. N Step 5: Increase j by one. If j is not equal to M × , repeat Step 2 2 until all blocks are processed.
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The proposed method can be decrypted without any computation and the secret is easily to be interpreted by the human perception. Users only need to gather two secret images to photocopy them onto transparencies and perform stack-to-see mechanism to get the first secret image. The second secret image can be extracted by turning over the first transparency and superimpose it onto the other one. Finally, the operation of decryption is performed to show the secrets by the meaningful transparencies.
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3. Experimental results
⎛ ⎞ 1122 ⎜1222⎟ ⎜2121⎟ ⎜2122⎟ ⎜2211⎟ ⎜ ⎟ ⎝2212⎠ 2221 2222
In this section, we conducted the simulation of the proposed scheme to show the performance. Fig. 4 shows the 512 × 512 binary secret images. Fig. 5 exhibits twelve 256 × 256 gray-level images used as cover images to achieve the goal of meaningful shares, i.e., Barbara, Baboon, Goldhill, Lena, Peppers, Sailboat, Bridge, Cameraman, Elaine, Tank, View, and Man. The result of twelve cover images preprocessed by the halftone technique is shown in Fig. 6. In this paper, we generate two meaningful transparencies to share two secret images at the same time via turning and stacking mechanism. Therefore, the scheme preserves the user-friendly property of visual secret sharing techniques. Moreover, the method which satisfies four general criteria for VSS scheme, that is, security, accuracy, computational complexity and shadow size, also called pixel expansion. The experimental results to demonstrate our achievements related to these criteria are presented in Sections 3.1, 3.2, 3.3 and 3.4.
⎞ ⎛ 1122 ⎟ ⎜1221 2112 ⎟ ⎜ ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222 ⎛ ⎞ 1122 ⎜1222⎟ ⎜2112⎟ ⎜2122⎟ ⎜2211⎟ ⎜ ⎟ ⎝2212⎠ 2221 2222 ⎛
2221
⎞ 1122 ⎜1221⎟ ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎟ ⎜ ⎝2212⎠ 2221 2222
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⎞ 1122 ⎜1222⎟ ⎜2122⎟ ⎜2211⎟ ⎜2212⎟ ⎠ ⎝ 2221 2222
Condition 1:black-pool, if 0 ≤ HW (MM y ) < 2, Condition 2:white-pool, if 2 ≤ HW (MM y ) ≤ 4,
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⎛ 2222
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into black-pool or white-pool. The distribution algorithm is performed under the following conditions.
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Table 3 The 16 combinations of encoding matrices for two symmetric pairs S = [ S 1 (i , j ), S 1 (i , N − j + i ), S 2 (i , j ), S 2 (i , N − j + i )].
(2)
where the function of HW (•) is to compute the number of non-zero pixel values in one block. Step 4: Based on the halftone cover image, the black or white pixel in the cover image for deciding the black-pool or white-
The security of our proposed scheme is based on two factors: the meaningfulness of shadows (or also called transparencies) to avoid suspicion from attacker and the randomness of selecting codewords in encoding matrices to form transparencies. Table 4 illustrates the experimental results of the proposed scheme with two meaningful shadows: Shadow1 and Shadow2. The first two columns list the shadows sized 512 × 512, in which we have encrypted two secret images into shadows with our designed codebook. Without any computation, we can superimpose Shadow1 onto Shadow2 to extract the first secret image as Fig. 4(a). By turning Shadow1 over with horizontal and stacking it onto Shadow2, the second secret image can be exposed as in Fig. 4(b). Here, the last two columns show the stacking results of two shadows. Furthermore, the probabilities distribution of codewords selected from the encoding matrix are fluctuated from 1/7 ≈ 14.2% (for the case of all pixels are BLACK) to 1/12 ≈ 8.3%, it is a very small variance to judge the full secret images. Therefore, no matter what codewords or sub-matrices are chosen, the secret images cannot be revealed.
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Fig. 5. 256 × 256 gray-level cover images.
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To achieve the accuracy of stacking results, our method preserves the opaque of secret images. In other words, to generate the encoding set, we check the entire Black pixels in the stacking results to form Table 2, and then create the encoding matrices by picking out satisfied encoding set from Table 2. Therefore, it can be seen from the stacking results in Table 4 that our proposed scheme completely reveals the original secret images. From the experiments, the stacking results can exactly show the intact of black pixel values in secret images. According to the codebook, two secrets can be revealed clearly. With the construction of the
codebook, the content of each combination is chosen in advance for guaranteeing that the black pixel can be completely retrieved from the stacked results.
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To demonstrate that the proposed scheme requires a very low computational cost, we analyze the scheme in two procedures: share construction procedure and revealing procedure.
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– In share construction procedure, we first generate the possible encoding sets. This step is to figure out all the combination of
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Fig. 6. 256 × 256 halftone cover images.
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the group of 4 pixels, thus, the time complexity of this step is O (n). The next step in this procedure is to find the suitable matching solution to form the encoding matrices. It is obvious that this step spends O (n). Therefore, these steps require very low time consuming. – In the revealing procedure, the secrets are constructed without any extra computations. We reveal the secret by simply turning and stacking steps.
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In summary, our scheme has low computational cost. Thus, it is suitable for real-time applications.
3.4. Pixel expansion
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From our share construction phase, the scheme shares two secret images at the same time without causing pixel expansion problem. In other words, the shadows generated by our scheme have the same size with the original ones. Finally, the comparisons between related works and the proposed method in terms of four different features are shown in Table 5. Only Fang’s method has to expand the size of original secret. Our scheme cannot only eliminate the defect of expanding original secret size, but also embed more than one secret into two
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Table 5 Performance comparisons with other schemes.
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Pixel expansion (times) Codebook needed Significance of shadows Decoding method The number of secret
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Naor and Shamir [1]
Fang [14]
Lee and Chiu [8]
Lin et al. [10]
Proposed scheme
4 Yes Meaningless Human Visual System 1
4 Yes Meaningful Human Visual System 1
1 No Meaningless Human Visual System 2
1 Yes Meaningless Human Visual System 2
1 Yes Meaningful Human Visual System 2
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4. Conclusions
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According to the designed codebook, an encoding technique with user-friendly shadows is proposed in this paper. This can greatly help reducing the potential risk from malicious attackers. In particular, the pixel expanding problem is absent from the proposed method. With the stack-to-see method for decoding two secrets, the whole decoding operation uses non-computation operation for combining two transparencies. Experimental results show that the complete black pixel value can be laid out to highlight the contrast to clarify the secret.
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[14] W.P. Fang, Friendly progressive visual secret sharing, Pattern Recognit. 41 (4) (2008) 1410–1414. [15] Y.C. Hou, Z.Y. Quan, Progressive visual cryptography with unexpanded shares, IEEE Trans. Circuits Syst. Video Technol. 21 (11) (2011) 1760–1764. [16] L. Feng, C.K. Wu, X.J. Lin, A new definition of the contrast of visual cryptography scheme, Inf. Process. Lett. 110 (2010) 241–246. [17] T.H. Chen, C.S. Wu, Efficient multi-secret image sharing based on Boolean operations, Signal Process. 91 (2011) 90–97. [18] C.C. Wu, L.H. Chen, A study on visual cryptography, M.S. thesis, Institute of Computer and Information Science, National Chiao Tung University, Hsinchu, Taiwan, 1998.
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Uncited references
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[3]
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References
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Jung-San Lee has worked as an associate professor in the Department of Information Engineering and Computer Science at Feng Chia University, Taichung, Taiwan. His current research interests include information security, image processing, and watermarking.
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transparencies. As to the other two schemes, even they can get rid of the problem of pixel expansion, they cannot offer meaningful shadows to prevent from potential risk.
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[1] N. Naor, A. Shamir, Visual cryptography, in: Advances in Cryptography Eurocypt, Springer-Verlag, Berlin, 1994, pp. 1–12. [2] A. Shamir, How to share a secret, Commun. ACM 22 (11) (1979) 612–613. [3] C.C. Thien, J.C. Lin, An image-sharing method with user-friendly shadow images, IEEE Trans. Circuits Syst. Video Technol. 13 (12) (2003) 1161–1169. [4] C.N. Yang, New visual secret sharing schemes using probabilistic method, Pattern Recognit. Lett. 25 (4) (2004) 481–494. [5] C.N. Yang, C.B. Ciou, Image secret sharing method with two-decoding-options: lossless recovery and previewing capability, Image Vis. Comput. 28 (12) (2010) 1600–1610. [6] D. Jin, W.Q. Yan, M.S. Kankanhalli, Progressive color visual cryptography, J. Electron. Imaging 14 (3) (2005) 033019-1–033019-13. [7] F. Liu, C.K. Wu, X.J. Lin, Colour visual cryptography schemes, IET Inf. Secur. 2 (4) (2008) 151–165. [8] K.H. Lee, P.L. Chiu, A high contrast and capacity efficient visual cryptography scheme for the encryption of multiple secret images, Opt. Commun. 284 (12) (2011) 2730–2741. [9] S. Cimato, R. De Prisco, A. De Santis, Colored visual cryptography without color darkening, Theor. Comput. Sci. 374 (1–3) (2007) 261–276. [10] S.J. Lin, S.K. Chen, J.C. Lin, Flip visual (FVC) with perfect security, conditionallyoptimal contrast, and no expansion, J. Vis. Commun. Image Represent. 21 (8) (2010) 900–916. [11] S.J. Shyu, K. Chen, Visual multiple secret sharing based upon turn and flipping, Inf. Sci. 181 (5) (2011) 3246–3266. [12] S.J. Shyu, Image encryption by multiple random grids, J. Pattern Recognit. 42 (7) (2009) 1582–1596. [13] S.J. Lin, J.C. Lin, VCPSS: a two-in-one two-decoding-options image sharing method combining visual cryptography (VC) and polynomial-style sharing (PSS) approaches, Pattern Recognit. 40 (12) (2007) 3652–3666.
Chin-Chen Chang is a Fellow of IEEE, a Fellow of IEE and a member of the Chinese Language Computer Society, the Chinese Institute of Engineers of the Republic of China, and the Phi Tau Phi Society of the Republic of China. His research interests include computer cryptography and image compression.
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Ngoc-Tu Huynh received the M.S. degree in 2010 from Feng Chia University. Since 2006, she has been a Lecturer of Department of Computer Science, College of Information Technology, Da Nang University, Vietnam. She is currently pursuing her Ph.D. in Information Engineering and Computer Science, Feng Chia University, Taichung, Taiwan. Her research interests include visual secret sharing, and image processing.
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Hsin-Yi Tsai has received the B.S. degree in computer science in 2012 from National Tsing Hua University, Taiwan. Her current research interests include information security and visual secret sharing.
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